Psionic power comes from within, while magic comes from without. Magic is the manipulation of external forces and the alteration of universal laws by use of formulae and props to create supernatural change, while psionics is the projection of internal energies of the mind, body and soul working in unison to create change in the world outside of the user's body.
Just think of Doctor Strange, who uses psionics as much as traditional arcane magic among his powers. Astral projection and telepathy have been described as totally deriving from his own energies instead of outside forces, while his spells call upon otherplanar powers like the Vishanti and the Faltine. (although that is a superhero reference, you can't get much mote wizardly than Doc Strange!)
Think of such things as Yogis and other Eastern mystics for your inspiration for psionics, instead of the European concepts of Hermetic magic. I have always equated psionics with ki, and consider them to be the same power, and count Monks as a psionic class (which was actually just talked about in a recent Mind's Eye article on the WotC D&D website.) Arcane magic in D&D is heavily based on the almost scientific, alchemistic style magic, while psionics are much closer to Eastern meditative systems of supernatural power.
And as to the people who have been asking why he wants to broaden his perspective and actually learn to accept psionics: you are actually asking why someone wants to overcome their prejudices and expand their horizons? That's completely bizarre. If you don't like psionics then fine, stay out of the thread and stick to your your narrow views of fantasy, but don't come in here dumping on those of us with enough of an imagination to include more than what Tolkien wrote about in our D&D games.